Loops and Legs in Quantum Field Theory

Session

Parallel 3

16 Apr 2024, 14:30

Martin Luther

Conveners

Parallel 3

• Andreas von Manteuffel (University of Regensburg)

Parallel 3

• Andreas von Manteuffel (University of Regensburg)

99. A new method for the reconstruction of rational functions

Xiao Liu (Oxford)

16/04/2024, 14:30

In this talk, I present a new method for the reconstruction of
rational functions through finite-field sampling that can significantly
reduce the number of samples required. The method works by exploiting all
the independent linear relations among target functions.
Subsequently, the explicit solutions of the functions can be efficiently
obtained by solving the linear system. As a first...

69. Learning Feynman integrals from differential equations with neural networks

Simone Zoia (CERN)

16/04/2024, 15:00

I present a new approach for evaluating Feynman integrals numerically. We apply the framework of physics-informed deep learning to train neural networks to approximate the solution to the differential equations satisfied by Feynman integrals. I discuss a proof-of-concept implementation, and showcase a number of one- and two-loop examples.

76. Selection rule of canonical differential equations from Intersection theory

Jiaqi Chen (Beijing Computational Science Research Center (CSRC))

16/04/2024, 15:30

Symbolology is the language that organizes the analytic structure of Feynman integrals and is encoded in the canonical differential equations. Using the d log-bases and simple formulas of intersection numbers, we give an algebraic procedure to compute the entries in the coefficient matrix of CDE, including the symbol letters and the rational coefficients. We also provide a selection rule to...

91. Evaluating Parametric Integrals in the Minkowski Regime without Contour Deformation

Thomas Stone (IPPP, Durham University)

16/04/2024, 16:30

Tools

In this talk, we present selected examples demonstrating an alternative approach to contour deformation for numerically computing loop integrals in the Minkowski regime. This method focuses on identifying singular hypersurfaces (varieties of the F polynomial) and mapping them to known points which can then be resolved by employing blow-ups/sector decomposition techniques, thereby avoiding the...

29. p-adic reconstruction of rational functions in loop calculations

Herschel Chawdhry (Florida State University)

16/04/2024, 17:00

Tools

The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In this talk I will present work using p-adic numbers to reconstruct rational functions in a compact form. I will apply this to examples such as rational functions appearing in non-planar 2-loop 5-point amplitudes.

64. Challenges of the large moment method

Carsten Schneider (RISC, Johnnes Kepler University Linz)

16/04/2024, 17:30

Tools

The large moment methods is a powerful tool to produce many coefficients of power series solutions of coupled systems of linear differential equations. This method with all its variants relies on the crucial observation that the coefficients can be described by (coupled systems) of linear recurrences. In this talk we will discuss various algorithmic challenges (uncoupling of the underlying...

16. Analytic Evaluation of Multiple Mellin-Barnes Integrals

Sumit Banik (University of Zurich & Paul Scherrer Institut)

16/04/2024, 18:00

Tools

I will discuss a novel approach based on the triangulation of point configurations to evaluate higher-fold Mellin-Barnes (MB) integrals in terms of hypergeometric functions. I will show that this new approach is computationally more efficient than the existing conic hull approach to evaluate MB integrals. As an application of this triangulation approach, I will first present new, simpler...